# Tricky derivative problem!

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• Mar 15th 2012, 10:15 AM
NotAMathmatician314
Tricky derivative problem!
I understand how to take the derivative of an equation with respect to a variable, say S, but what do I do when there are two variables involved? Here's the problem d/dx [3cos(x^2) - 4e^t]
• Mar 15th 2012, 10:23 AM
Kanwar245
Re: Tricky derivative problem!
Treat t as constant, so
Quote:

d/dx [3cos(x^2) - 4e^t]
= 3 d/dx cos(x^2) - 4 d/dx e^t
= -6x sin(x^2) - 4e^t x
• Mar 15th 2012, 10:42 AM
tom@ballooncalculus
Re: Tricky derivative problem!
Quote:

Originally Posted by Kanwar245
Treat t as constant

Correct. But then...

Quote:

, so

d/dx [3cos(x^2) - 4e^t]
= 3 d/dx cos(x^2) - 4 d/dx e^t
... the e^t is constant, so it might as well come out with the 4:

= 3 d/dx cos(x^2) - 4e^t d/dx 1

... but then the whole second term is a constant term and drops out...

= -6x sin(x^2)

... period.

As long as t isn't a function of x, or anything... the context of the problem here would help.
• Mar 15th 2012, 10:54 AM
NotAMathmatician314
Re: Tricky derivative problem!
What would it look like if t was a function of x?
• Mar 15th 2012, 10:59 AM
Kanwar245
Re: Tricky derivative problem!
my bad, I integrated the 2nd part!
• Mar 15th 2012, 12:27 PM
skeeter
Re: Tricky derivative problem!
Quote:

Originally Posted by NotAMathmatician314
What would it look like if t was a function of x?

then you'd need to use the chain rule.